We consider a Poisson process $\eta$ on a measurable space $(\BY,\mathcal{Y})$ equipped with a partial ordering, assumed to be strict almost everwhwere with respect to the intensity measure $\lambda$ of $\eta$. We give a Clark-Ocone type formula providing an explicit representation of square...

We consider a Poisson process [eta] on a measurable space equipped with a strict partial ordering, assumed to be total almost everywhere with respect to the intensity measure [lambda] of [eta]. We give a Clark-Ocone type formula providing an explicit representation of square integrable...

We consider the path Zt described by a standard Brownian motion in on some time interval [0,t]. This is a random compact subset of . Using the support (curvature) measures of [D. Hug, G. Last, W. Weil, A local Steiner-type formula for general closed sets and applications, Math. Z. 246...

In this paper we study asymptotic behaviour of marked point processes describing failure processes of repairable systems in which repair decisions depend on the past. Under natural conditions on system parameters such processes admit unique time stationary distributions and are ergodic....

Based on recent results on the exploitation of "drift criteria" for general state-space Markov processes, we derive rates of convergence for (moments of ) processes associated with a renewal process with common inter-renewal time distribution F. Some of the results are classical and some are...

We propose two general methods for coupling marked point processes (MPPs) on the real half-line that are explicitly formulated in terms of (canonical) compensators. These couplings are related to several results in the literature as compensator bounds for the total variation distance between two...